General Relativity and Gravitation, Vol. 21, No. 8, 1989 Asymmetric Collision of Gravitational Plane Waves: A New Class of Exact Solutions 1 D. Tsoubelis 2 and A. Z. Wang 2 Received October 20, 1988 A new three-parameter class of solutions to the Einstein vacuum equations is presented which represents the collision of a pair of gravitational plane waves. Depending on the choice of the parameters, one of the colliding waves has a smooth or unbounded wavefront, or it is a shock, or impulsive, or shock accom- panied by an impulsive wave, while the second is any of the above types. A sub- family of the solutions develops no curvature singularity in the interaction region formed by the colliding waves. 1. INTRODUCTION Thanks to the development of new techniques for integrating the corre- sponding field equations, several new analytic models representing the collision of gravitational plane waves have been added recently to the original collection which we owe to Szekeres [1, 2], Khan and Penrose [-3], and Nutku and Halil [4]. (For a recent review, see Ref. [5].). One such method was developed by Chandrasekhar and Ferrari [6] and relies on the similarity of space-times admitting two space-like Killing vectors to those admitting one space-like and one time-like Killing vector field. Another solution generating technique, not less fertile than the previous one, is due to Belinsky and Zakharov [7, 8] and is usually referred to as the method of solitons (for a very lucid comparative analysis of the above techniques, see Ref. [9]). The new models constructed by the two methods mentioned above 1 Expanded version of a talk presented at the Third National Workshop on Recent Develop- ments in Gravitation, September 12-16, 1988, Ioannina, Greece. 2 Department of Physics, Division of Theoretical Physics, University of Ioannina, P.O. Box 1186, GR 451 10 Ioannina, Greece. 807 0001-7701/89/0800-0807506.00/0 9 1989 Plenum Publishing Corporation